Quantitative strong unique continuation for elliptic operators -- application to an inverse spectral problem
Analysis of PDEs
2025-03-27 v4
Abstract
Based on the three-ball inequality and the doubling inequality established in [23], we quantify the strong unique continuation established by Koch and Tataru [21] for elliptic operators with unbounded lower-order coefficients. We also derive a uniform quantitative strong unique continuation for eigenfunctions that we use to prove that two Dirichlet-Laplace-Beltrami operators are gauge equivalent whenever their corresponding metrics coincide in the vicinity of the boundary and their boundary spectral data coincide on a subset of positive measure.
Keywords
Cite
@article{arxiv.2209.09549,
title = {Quantitative strong unique continuation for elliptic operators -- application to an inverse spectral problem},
author = {Mourad Choulli},
journal= {arXiv preprint arXiv:2209.09549},
year = {2025}
}